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What is Mathematics? And some history of Arithmetic

What is mathematics? How did it develop (at the 35,000 foot view)? What is mathematics good for? Should mathematics education begin with counting (natural numbers) or with measuring quantities (real numbers)? Did finance lead the Sumerians to invent arithmetic in 5000 BCE? How did the Italians revolutionize arithmetic and finance in the 13th century? When did the first computing revolution occur?

These questions come from Keith Devlin's fascinating, introductory, nearly 2 hour long video General Overview and the Development of Numbers. Watch the video, then come to discuss it and the broader questions it raises on Saturday the 28th of September from 11 AM to 1 PM.

In addition, we will discuss the future of the Math Counts meetup. What do you want the group to become? What are your interests in mathematics? Do you have topics, books, videos, or activities that you could help us organize?

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  • CJ F.

    For a broad almost unfocused topic, we did a good job exploring mathematics from many angles. Devlin's video gave just the right amount of prodding. Looking forward to next month's book discussion on Jame Gleick's "Chaos" and "The Golden Ratio" in November (based on video #2 in the Devlin course and "The Golden Ratio: The Story of PHI, the World's Most Astonishing Number" by Mario Livio).

    I look forward to engaging mathematics with you all again next month!

    September 28, 2013

  • CJ F.

    I got a discussion going with Keith Devlin:

    September 27, 2013

  • CJ F.

    Another thread in Devlin's video is What is mathematics good for? What is the importance of mathematics?

    In addition to the long story about arithmetic, Devlin cites Galileo's claim that math is the language of science and technology. He also claimed that math helps us understand and do things in the world. How so? And it lets us store bits in computers.

    He quotes Graciela Chichilnisky "Mathematics works for today's society like the fossil fuels worked for the industrial society. Today, to get energy, we don't burn fossil fuels. Now, to get knowledge, we use mathematics."

    He mentions its importance in movie making & ice skating.

    Did Devlin convince you that mathematics is important and useful? Do you have a better argument or evidence?

    September 27, 2013

  • CJ F.

    What is mathematics?

    Devlin gives an historical answer: it started with numbers, then added shape, then motion and space, then in the modern era it left computation behind and is now more about understanding relationships and concepts.

    He mentions the view that math is the study of abstract structure.

    He seems to put the most weight behind the view (which he has been promoting since the 1970s) that mathematics is the science of patterns. Does that work for you?

    Buckminster Fuller reported that MIT (probably in the 60s or 70s) defined mathematics as the science of structure and pattern in general. Is structure also important? Is Devin correct to focus on just "the science of patterns"?

    Wikipedia says "Mathematics is the abstract study of topics such as quantity (numbers), structure, space, and change."

    What do you think?

    Is this "science of patterns" view the way we should present mathematics to others? To children?

    What is your favorite definition of mathematics?

    September 25, 2013

    • CJ F.

      Brad, exactly those are the questions. Bucky Fuller had his answers. Mathematics as an omnibus field has many, many answers some of which are contradictory or at least paradoxical. At the meetup, we will discuss people's understanding and work to further the conversation on these deep questions.

      September 27, 2013

  • CJ F.

    Devlin cites archeological evidence that the history of arithmetic began with the need to keep track of debts in Sumeria circa 5000 BCE (Devlin calls it money which wasn't invented until 600 BCE, so he is technically wrong). Then he looks in some depth at how Leonardo Pisano filias Bonaci (aka Fibonacci) launched the first computing revolution in 1202 in Europe with his mammoth "Liber abbaci" ("Book of Calculation") followed by a popularizing book in Italian that spurred the modern era of European finance.

    Many cite Luca Pacioli and his famous 1494 book "Summa de arithmetica" as the origin of modern finance in the Renaissance, but Pacioli himself admits in the Summa that most of it comes from Leonardo Pisano. Pacioli's book is widely printed, so his role becomes exaggerated.

    Devlin's fascinating story shows the epic role of mathematics in shaping modern civilization. What do you take away from this history of mathematics, arithmetic, computation, and finance? How does it affect you?

    September 27, 2013

  • CJ F.

    In the Devlin video, he very briefly discusses the question of whether math describes the actual universe or is an artifact of the human cognitive system. Devlin thinks that neither view is accurate.

    This fascinating PBS Idea Channel video goes into the question in more depth: The video is 8 minutes long, but only the first 6 minutes address the question. If you all are interested in discussing this in more depth on Saturday (or here in the comments), watch the video here:

    Does math actually describe the Universe?

    September 24, 2013

  • Martin C.

    I liked Devlin's talk, especially the discussion on Fibonacci. I do have some issues with the talk.

    The Greeks deserve more credit than he gave them. The exploration of proofs and Euclid's concept of axiomatization were unprecedented. See, for example, Alan Cromer's book Uncommon Sense -

    There was no discussion of non-Euclidean geometry, which is generally believed to have started the change in attitude toward math in the 19th century. What non-Euclidean geometry did was to separate math from science, leading to math becoming a self-contained discipline.

    I look forward to discussing mathematics. I would also be interested in talking about how math should be taught. Two areas of math I would like to explore are network theory and graph theory.

    1 · September 20, 2013

    • CJ F.

      Martin, I too was disappointed that Devlin mostly skipped geometry and non-Euclidean geometry.

      I look forward to discussing mathematics and how it should be taught too.

      Are there any general or popularizing books on networks or graph theory that you can recommend?

      I look forward to seeing you again next Saturday.

      September 21, 2013

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